On blow-up conditions for solutions of higher order differential inequalities

ABSTRACT

For differential inequalities of the form $$\sum _{|\alpha |=m}{(-1)}^m{\partial }^{\alpha }{a}_{\alpha }(x,u)\ge b(x){|u|}^{\lambda }\text{in}{\mathbb{R}}^n,n\ge 1,$$

where $a_{\alpha }$ and b are some functions, we obtain conditions guaranteeing that any solution is identically equal to zero. We construct examples which show that the obtained conditions are sharp.

KEYWORDS:

• Higher order differential inequalities
• nonlinear inequalities
• entire solutions

AMS SUBJECT CLASSIFICATIONS:

• 35B44
• 35B08
• 35J30
• 35J70

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the second author is supported by RUDN University [Project 5-100].